Solving Multi-Leader-Follower Games by Smoothing the Follower’s Best Response

Event Sponsor: 
Mathmatics and Computer Science Division Seminar - LANS
Start Date: 
Sep 21 2018 - 10:30am
Building 240/Room 4301
Argonne National Laboratory
Anna Thuenen
Speaker(s) Title: 
RWTH Aachen University

The multi-leader-follower game is a particular subset of classical game theory. These models serve as an analytical tool to study the strategic behavior of individuals in a noncooperative manner. In particular, the individuals (players) are divided into two groups, namely the leaders and the followers, according to their position in the game. Mathematically, this leads to optimization problems with optimization problems as constraints. The challenge in leader-follower problems arise due to possible nonsmoothness in the constraints.

We derive the best response function of the follower which we regularize using a suitable smooth regularizer. We discuss existence of Nash equilibria of the smoothed problems and deduce a numerical algorithm based on the smooth formulation. We further present an update of the primal variables for efficient computation. Finally, we present numerical results to illustrate our approach and give an outlook to future research.

Miscellaneous Information: 

This seminar will be streamed. See details at

Please click here [schedule.ics] to add this event to your calendar.

Google Calendar:

Upcoming Seminars
July 25, 2018, "Summer Argonne Student Symposium (SASSy) Part I", LANS Summer Students
August 1, 2018, "Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information" Siqian Shen, Associate Professor, Department of Industrial & Operations Engineering, University of Michigan
August 8, 2018, "SASSy Part II" LANS Summer Students
August 15, 2018, "TBA" Wissam M. Sid-Lakhdar, Postdoctoral Fellow, LBNL
August 22, 2018, "SASSy Part III" LANS Summer Students
August 29, 2018, "TBA" Selin Sariaydin, Postdoctoral Appointee (XSD/ANL)
September 5, 2018, "TBA" Dongwook Lee, Associate Professor, Applied Mathematics & Statistics, UC Santa Cruz
September 19, 2018, "TBA" Emil Constantinescu, Computational Mathematician (MCS/ANL)
October 1, 2018, "Advances in bounding methods for use in global optimization" Kamil Khan, Assistant Professor, Department of Chemical Engineering, McMaster University
October 17, 2018, "TBA" Kevin Gimpel, Assistant Professor, Toyota Technological Institute at Chicago
October 24, 2018, "TBA" Dmitriy Drusvyatskiy, Assistant Professor, Department of Mathematics, University of Washington